Abstract
In this paper, we describe the construction of new examples of self-translating surfaces under the mean curvature flow. We find the new surfaces by desingularizing the intersection of a grim reaper and a plane to obtain approximate solutions, then we solve a perturbation problem to find the exact solutions. Our work is inspired from Kapoulea' construction of minimal surfaces but differs from it by our more abstract and direct study of the linear operator, via Fredholm operators.
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